On The Expected Penalty Function For A Class Of Continuous Renewal Process With Time-dependent Claim Sizes

In actuarial literature the classical compound possion risk model is the continuous timerenewal risk process which has been paid much attention. In recent years, actuaries extend theclassical compound poisson risk models to different aspect and obtain many meaningfulresults. In this thesis we propose some generalized compound poisson processes withdependence structure and investigate some related ruin problems.This thesis is divided into four chapters:The first chapter begins with a brief description of the ruin theory of risk theory and itscore content, then reviews some classical results for the compound poisson risk model andGerber-Shiu function. Finally, the main work of the thesis are introduced briefly.Chapter two studies integral equation of Gerber-Shiu function and analysis of the integralequation.Firstly,the part begins the definition of a new variable,then a new integral equationis obtained,and some mathematic characteristics of integral equation is analyzed.Finallyanother form of expression of intergral equation is obtained.In the third chapter we study some discounted joint desity functions of ruinrelatedquantities.Firstly a proper penalty function is given,then some discounted joint and marginaldesity functions of ruinrelated quantities can be obtained.In the last chapter we study a class of the continuous delayed renewal risk process withtime-dependent claim sizes, and results related to the ordinary process are derived as well.Forthe generalized Gerber-Shiu function in this model, an integral equation for the discountedjoint desity function is derived in terms of the corresponding generalized Gerber-Shiufunction in the ordinary model.